{
  "id": 5483,
  "curve_key": "-4752:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "99",
    "0"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 25.398962583127442,
  "faltings_height": 0.18482062690211062,
  "conductor": "34848",
  "bad_primes": [
    "2",
    "3",
    "11"
  ],
  "discriminant": "-62099136",
  "regulator": "1.65402186404476473626042993306057742964569",
  "points": [
    [
      "3",
      "18"
    ],
    [
      "12",
      "54"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + 99x. Found in a bounded exact small-coefficient sweep over every nonzero integer A with -300 <= A <= 300 in y^2 = x^3 + Ax. Each curve was exactly minimalized and compared by c4:c6 identity against the current ICARM database.\r\n\r\nPARI/GP 2.17.4 returned rank bounds [2,2], rational torsion Z/2Z generated by [0,0], conductor 34848 and minimal discriminant -62099136. Exact quadratic-character certification at 9 good primes gives an F_2 matrix of rank 3 with torsion-row rank 1, proving the two submitted points independent modulo torsion.\r\n\r\nNo novelty claim is made beyond absence from the checked ICARM snapshot and this bounded search.",
  "created_at": "2026-10-22 09:55:36",
  "updated_at": "2026-10-22 09:55:36"
}